Some characteristics of the stagnation stage in the...

D. PANTIĆ, S. BANKOVIĆ, M. MEDAREVIĆ, S. OBRADOVIĆ

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Turk J Agric For35 (2011) 367-378© TÜBİTAKdoi:10.3906/tar-1002-654

Some characteristics of the stagnation stage in the development of silver fi r (Abies alba Mill.) trees in selection forests in Serbia

Damjan PANTIĆ*, Staniša BANKOVIĆ, Milan MEDAREVIĆ, Snežana OBRADOVIĆDepartment of Forest Management Planning, Faculty of Forestry, University of Belgrade, Kneza Višeslava 1,

11 030 Belgrade - SERBIA

Received: 01.02.2010

Abstract: A period of stagnation in silver fi r development has been recorded in all felled trees in selection forests of Serbia (233 trees on Mt. Goč and 451 trees on Mt. Tara). In the selection forests on Mt. Goč, the stagnation stage ranges between 40 and 330 years, but on Mt. Tara, it ranges from 15 to 185 years. It was concluded that the duration was caused not by the ecological and productivity potential (site class) of the soil for fi r development, but primarily by the growth space, resulting from the application of single-tree selection or group selection systems. It was also found that the duration of latent state and tree sizes attained over that phase (except for height, and that was to a lesser extent) did not aff ect the silver fi r tree development in the post-stagnation period.

Key words: Selection forest, Serbia, silver fi r, stagnation stage

Research Article

* E-mail: [email protected]

IntroductionUneven-aged forest management has a signifi cant

role in forestry in central Europe (Mitscherlich 1961; Mlinšek 1968; Schütz 1989; Klepac 1995) and parts of southeastern Europe. Over the last few decades, higher public awareness of the forest ecosystem multifunctionality has made it a signifi cant option (Schütz 1997) in the integration of forest protection, social production, and other aspects of forest management. However, the management of selection forests in these areas of Europe has recently encountered numerous problems, which are refl ected in the structural changes (Schütz 1975, 1992; Korpel 1982; Boncina et al. 2002), the death of silver fi r (Larsen 1986; Ell and Luhmann 1996; Oliva and Colinas 2007; Elling et al. 2009), the change in dominant tree species compared to beech,

the decrease in silver fi r percentage in the mixture as the carrier of the selection structure (Boncina et al. 2003), and in the diffi culties in achieving natural regeneration (Korpel 1985; Andrzejzyk et al. 1987). Th e individual, and, much more oft en, the synergic eff ects of these problems at some sites, throw into question the capacity of selection forests to fulfi ll the numerous functions in the group of the assigned protection, social and production functions. Th e starting point in the identifi cation of adequate management procedures to address these problems is the study of biological potential (Bagnaresi et al. 2002) and the development regularities and dynamics (Banković 1981) of the species incorporated in selection forests. Th is is especially relevant to silver fi r, as the tree species is narrowly related to selection management, the method which has always been and


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will remain one of the most signifi cant systems of silver fi r management.

Th e study of the dynamics of silver fi r and its characteristic development on Mt. Goč and Mt. Tara, the mountains with the most important complexes of selection forests in Serbia, which have already been managed for 50 years by the principles of the control method (Biolley 1920; Schaeff er et al. 1930; Miletić 1951; Milojković 1962; Obradović 2008), emphasizes the growth stagnation in fi r development as the general characteristic. Latent state occurs as a consequence of the specifi c structure of selection forests, and in this sense, of the lack of growing space (primarily the lack of light from above) in the earliest phases of tree development (in the seedling stage), and biological features and capacities of tree species to survive in such conditions. Th is means that aft er a long period of suppression, silver fi r, which falls in the category of an extremely shade tolerant tree species (Šafar 1963; Stanescu et al. 1997), is capable of reforming full growth aft er favorable light conditions have been created by felling, snow break, uprooting, etc., and the morphological traces of the time spent in deep shade disappear gradually with advancing age (Stojanović and Krstić 2008).

Th e opinion that each tree in a selection forest has special laws of development (Biolley 1920), i.e. that this stand form off ers hundreds of very favorable laws governing the tree development (Badoux 1949), indicates that the period of growth stagnation depends primarily on the silver fi r’s biological characters, such as the maximal possible period of shade tolerance with the continuation of normal development in favorable environmental conditions and on management procedures, such as regeneration felling of suppressed trees. In this sense, the fi rst objective of this research was to identify the maximal possible length of stagnation period aft er which silver fi r can continue its normal development.

Th e development of individual trees of a species depends primarily on the site and stand conditions. Taking into account this general assumption and the biological characters of silver fi r trees, it can be presumed that the length of tree stagnation is more dependent on stand conditions (growth space of individual trees) than on site conditions. For this reason, the second objective of this research was to

assess the eff ect of site conditions on the length of the silver fi r stagnation stage.

Given that silver fi r trees are subject to growth stagnation, the question is whether the stagnation has a major eff ect on fi r tree development in the post-stagnation period. Magin (1959) concludes that the length of stagnation stage does not have a signifi cant eff ect on the subsequent development of silver fi r trees. However, aft er studying the development trends of silver fi r to assess the productivity of ecological units in the selection forest on Mt. Goč, Banković (1981) reported that the stagnation stage and the tree sizes attained over that period infl uenced the development of silver fi r trees in the post-stagnation period. Th erefore, the third objective of this research was to analyze the eff ect of the stagnation stage (its length and the tree sizes attained over that period) on the later development, specifi cally on the development of silver fi r trees in the post-stagnation period.

Beginning with the above statements and tasks, the following are the initial hypotheses of this research:• Silver fi r falls in the category of an extremely

shade tolerant tree species;• Site conditions do not have a major eff ect on the

analyzed elements of the stagnation stage (its length and tree sizes attained over that period);

• Th ere is no statistically signifi cant correlation between silver fi r development over post-stagnation and stagnation periods.

Materials and methodsStudy areaMt. Goč forests are located between latitudes

43°30ʹ and 43°35ʹN and longitudes 18°15ʹ and 18°30ʹE (Figure 1). Th e parent rock consists of old Palaeozoic schists with a low degree of metamorphism, contact metamorphic rocks, marble, granodiorites, andesites, dacites, and serpentinitized dunites. Th e soils are classifi ed as sierozem, black soils, brown soils, leached brown soils and podzols. A humid climate prevails in the region. Th e average annual air temperature is 7.3 °C, relative air humidity is 81%, precipitation is 1010 mm, and duration of sunny periods is 1938 h (Banković 1981; Jović et al. 1999).


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Based on the research of site-class potentials for silver fi r development, the following forest types were defi ned in silver fi r and beech selection forests on Mt. Goč (Banković 1981):• Forest of silver fi r and beech (Abieti-Fagetum

typicum) on deep (81-120 cm) and very deep (> 120 cm) acid brown soils on granodiorites and quartz-diorites (I site class);

• Forest of silver fi r and beech (Abieti-Fagetum drymetosum) on shallow (16-40 cm) and medium deep (41-80 cm) acid brown soils on granodiorites and quartz-diorites (II site class);

• Forest of silver fi r and beech (Abieti-Fagetum drymetosum) on shallow (16-40 cm) and medium deep (41-80 cm) acid brown soils on schists and contact metamorphic rocks (III site class);

• Forest of silver fi r and beech (Abieti-Fagetum serpentinicum typicum) on skeletal brown soils to leached brown soils on serpentinite (IV site class).

Mt. Tara forests are located in the far west of Serbia, between latitudes 43°52ʹ and 44°02ʹN and longitudes 19°15ʹ and 19°38ʹE (Figure 1). Th e basic parent rocks consist of serpentinitized peridotites, Middle and Upper Triassic limestones, amphibolites and Tertiary sediments. Th e most represented soils occur on limestone (calcareous black soil, rendzina, brown soils on limestone, terra fusca, illimerized soils, and leached terra fusca), on serpentinite (humus-siliceous soils, ranker, and eutric brown soils), and less on siliceous rocks (dystric humus-siliceous soil, dystric ranker, and acid brown soils). A continental mountainous climate approximating the more humid variant of a subalpine climate prevails in the area. Th e average annual air temperature is 7.9 °C, relative air humidity is 83%, precipitation (with a substantial percentage of snow) is 977 mm, and duration of sunny periods is about 1700 h (Medarević et al. 2002, 2005; Obradović 2008).

Forest on

Forest onthe Tara Mountain

the Goc Mountain

Hungary

Novi SadCroatia

BeogradRomania

Bulgaria

Pristina

AlbaniaFYR Macedonia

Montenegro

KragujevacBosania andHercegovina

Nis

N

SW E

Figure 1. Location of the study areas. Th e most signifi cant complexes of selection forests in Serbia (Mt. Goč and Mt. Tara).


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Th e following forest types were defi ned based on the study of soil, phytocoenology, and the productivity development of silver fi r, spruce, and beech selection forests on Mt. Tara (Medarević et al. 2005):

• Forest of silver fi r, spruce, and beech (Piceo-Abieti-Fagetum typicum) on medium deep (41-80 cm) and deep (81-120 cm) brown soils on limestone (I site class);

• Forest of silver fi r, spruce, and beech (Piceo-Abieti-Fagetum drymetosum) on very shallow (< 15 cm) and shallow (16-40 cm) brown soils on limestone (II site class);

• Forest of silver fi r, spruce, and beech (Piceo-Abieti-Fagetum) on skeletal-karst soil on limestone (III site class).

As already stated, the Mt. Goč and Mt. Tara forests are the most signifi cant and the most valuable complexes of selection forests in Serbia, and for that reason, among others, they were selected for this research.

Data collection and processingSatellite images of Mt. Goč and Mt. Tara show a

square form grid network, the sides of which are 400 m. Th e centers of circular plots of a 10 m radius are in the intersection points of the cluster network. A circular plot which, based on the imagery data and additional information from the Forest Information System data base in Serbia, is classifi ed as a selection stand of silver fi r and beech (silver fi r, spruce, and beech, are assigned identifi cation numbers and the coordinates of its center are identifi ed). If a sample plot is in a clearing, in even-aged stands or stands of other tree species, etc., it is excluded from the sample. Th is procedure ensures that the sample covers all forest types (site classes) in which silver fi r occurs in the study sites, as well as the selection stands in diff erent development phases within each forest type (selection forest in construction, in the optimal phase, and in degradation). Th is method ensures the representative sample as a necessary prerequisite for valid conclusions.

In the fi eld, circular plots were detected using a GPS receiver, aft er which the center of the sample plot was temporarily marked. Th e distances of the trees in the circle to the nearest neighbors were measured using a Vertex III hypsometer with transponder-by ultrasonic distance meter. Diameters at breast height (DBH) were measured for each silver fi r tree in the circle, as was the length, i.e. height (H), aft er tree felling and debranching. Th e felled trees were cut into disks: on the stump (0.3 m), at breast height (1.3 m), and then at lengths of 2 m (3.3 m, 5.3 m, 7.3 m, etc.).

Th e stem disks were analyzed using LINTAB 4 tree-ring measuring, with TSAP soft ware. Tree age was calculated by counting growth rings on the disk taken at the stump. Ages ranged between 130 and 380 years on Mt. Goč and between 49 to 305 years on Mt. Tara. Based on the diameters at the end of the ten-year periods which were marked on each disk from the periphery towards the center, on the height (length) at which the disks were taken, and on the number of growth rings, the calculated data made it possible to draw the lines of development and diameter, height and volume increments of each felled silver fi r tree, using Tree Analysis soft ware (Banković and Pantić 2006). Silver fi r development at diff erent sites will be the subject of a special analysis. Th is paper focuses on only 1 phase in the development-the stagnation stage. Th us, the stagnation stage was diff erentiated from the post-stagnation period. Th e criteria for the diff erentiation of these two phases in silver fi r development were growth ring width on disks at breast height, i.e. current diameter increment (Ferlin 2002), and current height increment (Banković 1981). Growth ring width above 1 mm, that is, the current diameter increment above 2 mm and the current height increment above 0.125 m, were the indicators that the tree was out of the stagnation stage. Th e tree sizes in the latent state (dbh and h) were calculated based on the duration of the stagnation stage (t) from the lines of diameter and height growth. Th erefore, the data for 233 fi r trees were calculated on Mt. Goč, and for 451 fi r trees on Mt. Tara, with the forest type structure (site classes) presented in Tables 1 and 2.


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Th e trees in the Mt. Goč stands are distributed by the single-tree selection system and on Mt. Tara by group selection. To confi rm the visual assessments, the information in the Forest Information System data base in Serbia, and the results of previous research at these localities (Stajić and Vučković 2006), the spatial distribution of trees in the study stands (random, group, or uniform) and the structure in the nearest neighborhood were calculated using the Clark-Evans index. Th e average empirical distance to the nearest neighbor was compared to the average theoretical distance to the nearest neighbor in random distribution. Th e ratio of these 2 values is the Clark-Evans index (CEI). Th e deviation of CEI from 1 was verifi ed by the value of c (c is the standard variance of the normal curve) at the 95% confi dence level (Clark and Evans 1954).

Th e diff erences in average lengths of the stagnation stage between site classes and average tree sizes attained over that period in the study areas were tested by one-way ANOVA and LSD tests at the 95% confi dence level. Th e forms and intensities of simple relation between tree sizes in the post-stagnation period (DBH and H), the duration of the stagnation stage (t), and tree sizes attained over the latent state (dbh and h) were determined using correlation analysis (Correlation Matrix and its graphical equivalent Scatterplot Matrix) and regression analysis. Th e value of the correlation coeffi cient was ranked using the very precise Roemer-Orphal scale (0.0-0.10, no correlation; 0.10-0.25, very weak; 0.25-0.40, weak; 0.40-0.50, modest; 0.50-0.75, strong; 0.75-0.90, very strong; 0.90-1.0, full correlation) at the 95% confi dence level. Th e above statistical analyses were performed using STATGRAPHICS Plus 5.1 soft ware for Windows.

Table 1. Duration of the stagnation stage, average sizes of silver fi r trees in the stagnation stage and average sizes of silver fi r trees in the post-stagnation period (at felling) in the Mt. Goč selection forests.

Site class Number of analyzed trees

Duration of stagnation staget (years)

Average tree sizes in stagnation stage

Average tree sizes in post-stagnation period

Min Max Average dbh (mm) h (m) DBH (mm) H (m)

I 68 60 260 150 153.1 10.1 705.0 36.1

II 46 40 330 148 155.7 10.7 652.0 32.4

III 59 50 210 151 160.2 10.3 597.0 29.7

IV 60 60 310 154 159.7 10.4 501.0 26.1

In general for Mt. Goč 233 40 330 151 157.2 10.4 613.8 31.1

Table 2. Duration of the stagnation stage, average sizes of silver fi r trees in the stagnation stage and average sizes of silver fi r trees in the post-stagnation period (at felling) in the Mt. Tara selection forests.

Site class Number of analyzed trees

Duration of stagnation staget (years)

Average tree sizes in stagnation stage

Average tree sizes in post-stagnation period

Min Max Average dbh (mm) h (m) DBH (mm) H (m)

I 219 15 122 55 71.4 6.1 536.0 31.5

II 189 16 185 53 72.6 6.5 490.0 27.2

III 43 18 102 54 74.1 6.2 375.0 23.9

In general for Mt. Tara 451 15 185 54 72.7 6.3 467.0 27.5


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ResultsLength of stagnation stage Previous studies of diff erent silver fi r aspects

(ecology, biology, growth dynamics, productivity, stand structure, etc.) reported diff erent maximal durations of the stagnation stage, either as a conclusion or as a secondary result. Our research shows that the length of growth stagnation in silver fi r development in the single-tree selection system on Mt. Goč ranges between 40 and 330 years and between 15 and 185 years in the group selection system on Mt. Tara.

Th e average stagnation stage of silver fi r on Mt. Goč is 151 years and during that period the trees attained 157.2 mm in diameter and 10.4 m in height on average. So the average diameter increment is 1.04 mm, and the average height increment is 0.069 m (Table 1). In selection forests on Mt. Tara, the silver fi r latent state is 54 years on average. During that period, the trees reach a diameter at breast height of 72.7 mm and a height of 6.3 m. Th erefore, the average diameter increment is 1.35 mm, and the average height increment 0.117 m (Table 2).

Th e above values of diameter and height increments across the stagnation period point to the extraordinary capacity of silver fi r both to survive in the conditions of full shade, drastically reducing its growth, and to preserve its capacity to continue normal development aft er 330 years, when a more favorable light regime has been released. Th ese characters make silver fi r an extremely favorable species for the application of single-tree selection or small-group selection systems.

Eff ect of site conditions on the length of stagnation stage

Th e results of one-way ANOVA show that there are no statistically signifi cant diff erences in the average lengths of silver fi r stagnation in diff erent forest types (site classes) on Mt. Goč (F3,229 = 0.97, P = 0.4332). Th is leads to the conclusion that site conditions in selection forests on Mt. Goč do not have a major eff ect on the duration of the latent state in silver fi r development, and that it mostly depends on stand conditions, namely, growth space. Th e same could also be concluded for the average values of tree diameter (F3,229 = 1.74, P = 0.1013) and height (F3,229 = 0.12, P = 0.9439) attained during the stagnation.

Th e diff erences between the sites in selection forests on Mt. Tara also do not have a statistically signifi cant eff ect on the average length of the silver fi r stagnation stage (F2,448 = 0.70, P = 0.5168), or on the average tree diameter (F2,448 = 0.82, P = 0.4621) and height (F2,448 = 0.33, P = 0.7221) attained in that period.

Th e comparative analysis of the values in Table 1 (Mt. Goč) and Table 2 (Mt. Tara) shows that there are signifi cant diff erences between these 2 localities in all the analyzed parameters of stagnation stages. As the site potential for silver fi r development on Mt. Goč is signifi cantly higher than that on Mt. Tara, it could be supposed that it is the cause of the above diff erences between the 2 localities. However, it was confi rmed that site conditions in the localities do not have a statistically signifi cant eff ect on the analyzed values of the stagnation stage, and so it is more logical to conclude that the diff erences between Mt. Goč and Mt. Tara result from the activities of other factors with a strong eff ect on tree development. Th e 2 factors which aff ect the growth space are primarily the stand origin and the applied selection system. On Mt. Goč, signifi cant harvesting of silver fi r and beech selection forests started 65 years ago, and so the forests still have a primeval forest character. In selection forests of silver fi r, spruce, and beech on Mt. Tara, signifi cant harvesting started 230 years ago, and so these forests can be considered “regular” selection forests. Furthermore, the system applied in Mt. Goč selection forests is single-tree selection (random distribution of trees CEI = 0.94; c = -0.44) and the system applied on Mt Tara is group selection (group distribution of trees CEI = 0.83; c = -2.97). Th ese 2 systems create unequal conditions for the development of silver fi r trees; the former creates a lesser amount of growth space, and the latter creates a much larger space for the development of suppressed trees, which are subject to growth stagnation due to the absence of light. In the selection forests on Mt. Goč, the virgin-forest character and the applied single-tree selection system are most probably the 2 basic causes of the substantially higher values of growth stagnation parameters, compared to selection forests on Mt. Tara.


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Eff ect of the stagnation stage on silver fi r development in the post-stagnation period

Th e high variability of the study elements (DBH, H, t, dbh, h) in the Mt. Goč selection forests (Figure 2) makes the linear correlation between them practically non-existent. Th is conclusion is also confi rmed by the correlation matrix (Table 3), which shows the correlation coeffi cient in the linear correlation type DBH = f (t) 0.0261 (P = 0.8105), in DBH = f (dbh) 0.0767 (P = 0.4800), and in H = f (t) -0.0264 (P = 0.8085), whereas in H = f (h), it amounts to 0.0607 (P = 0.5764). As for the nonlinear forms of these correlations (Table 4), the values of correlation

coeffi cient indicate the absence or presence of very weak correlation between the analyzed variables. An exception is the correlation type H = f (h) which is weak in the second order polynomial and amounts to 0.3146 (P = 0.0125). Th e above facts lead to a conclusion that the length of the stagnation stage and the tree sizes attained over that period (except for height) do not have a statistically signifi cant eff ect on the development of silver fi r trees in the post-stagnation period.

Th e Mt. Tara selection forests are also characterized by a high variability of data (Figure 3), and so there is practically no linear correlation between the study

DBH

H

t

dbh

h

Figure 2. Scatterplot matrix of the variables in the Mt. Goč selection forests.

Table 3. Correlation matrix of the variables in the Mt. Goč selection forests.

DBH H t dbh h

DBH 0.7336(0.0000)

0.0261(0.8105)

0.0767(0.4800)

-0.0118(0.9136)

H 0.7336(0.0000)

-0.0264(0.8085)

0.0599(0.5813)

0.0607(0.5764)

t 0.0261(0.8105)

-0.0264(0.8085)

0.7077(0.0000)

0.6939(0.0000)

dbh 0.0767(0.4800)

0.0599(0.5813)

0.7077(0.0000)

0.8803(0.0000)

h -0.0118(0.9136)

0.0607(0.5764)

0.6939(0.0000)

0.8803(0.0000)

Correlation Coeffi cient (P-Value)


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variables, which is also evident from the correlation coeffi cients and their statistical signifi cance presented in the correlation matrix (Table 5). In other tested functions (Table 6), correlation coeffi cients range within the Roemer-Orphal scale indicating the absence or presence of a very weak correlation between the analyzed variables. Just as in the case of Mt. Goč, the exception to the general assessment is

the correlation H = f (h), which is weak in the second order polynomial (R = 0.3359) and is statistically signifi cant at the signifi cance level above 95% (P = 0.0118). Consequently, in the conditions of Mt. Tara, the stagnation stage and the tree sizes attained over that period (except height) do not have a statistically signifi cant eff ect on the later development of silver fi r trees.

Table 4. Test results of nonlinear correlation between the variables in the Mt. Goč selection forests.

DBH = f (t) DBH = f (dbh) H = f (t) H = f (h)

R P R P R P R P

Exponential 0.0308 0.7769 0.0739 0.4965 0.0038 0.9721 0.0757 0.4856

Reciprocal - y -0.0371 0.7330 -0.0726 0.5041 -0.0346 0.7501 -0.0919 0.3972

Reciprocal - x -0.1265 0.2430 -0.1694 0.1168 -0.0016 0.9883 -0.1780 0.0993

Double Reciprocal 0.1209 0.2648 0.1446 0.1815 0.0619 0.5688 0.2000 0.0632

Logarithmic - x 0.0947 0.3827 0.1437 0.1841 -0.0080 0.9417 0.1287 0.2347

Multiplicative 0.0960 0.3765 0.1374 0.2045 0.0240 0.8251 0.1433 0.1854

Square Root - x 0.0639 0.5567 0.1063 0.3273 -0.0163 0.8810 0.0947 0.3830

Square Root - y 0.0283 0.7950 0.0752 0.4890 -0.0115 0.9161 0.0680 0.5312

S-Curve -0.1244 0.2510 -0.1598 0.1392 -0.0319 0.7690 -0.1898 0.0783

Polynomial - order 2 0.2388 0.0849 0.1348 0.4632 0.0910 0.7052 0.3146 0.0125

R - Correlation Coeffi cientP - P-value from the ANOVA

DBH

H

t

dbh

h

Figure 3. Scatterplot matrix of the variables in the Mt. Tara selection forests.


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DiscussionTh e study of biological potential, dynamics and

laws of development of tree species is one of the necessary instruments for addressing numerous problems occurring in European selection forests. A modest contribution to this task is the study of some characteristics of stagnation stage in the development of silver fi r trees in selection forests in Serbia.

Th is research shows that silver fi r can survive in deep shade for as long as 330 years, retaining its strong capacity for normal development in the conditions of a more favorable light regime. Assman

(1961) reported a period of only a few decades, while Milojković and Mirković (1955) reported more than 100 years in Mt. Tara conditions, and the same duration was reported also by Schütz (1969, 2001, 2002) and Jaworski and Zarzycki (1983). Th e upper limit of the silver fi r latent state is 140 years in Gorski Kotar (Frančisković 1938), 189 years in selection forests of Slovenia (Ferlin 2002), and Šafar (1963) reports as many as 200 years. Compared to the stagnation stages reported by the above authors for European selection forests, a latent stage duration of 330 years is a considerably longer period and it

Table 5. Correlation matrix of the variables in the Mt. Tara selection forests.

DBH H t dbh h

DBH 0.6990(0.0000)

0.0125(0.8698)

0.0591(0.4384)

0.0160(0.8345)

H 0.6990(0.0000)

-0.0988(0.1531)

-0.0491(0.5199)

0.0005(0.9948)

t 0.0125(0.8698)

-0.0988(0.1531)

0.7090(0.0000)

0.7068(0.0000)

dbh 0.0591(0.4384)

-0.0491(0.5199)

0.7090(0.0000)

0.8790(0.0000)

h 0.0160(0.8345)

0.0005(0.9948)

0.7068(0.0000)

0.8790(0.0000)

Table 6. Test results of nonlinear correlation between the variables in the Mt. Tara selection forests.

DBH = f (t) DBH = f (dbh) H = f (t) H = f (h)

R P R P R P R P

Exponential 0.0165 0.8293 0.0584 0.4442 -0.0824 0.2797 0.0127 0.8676

Reciprocal - y -0.0233 0.7700 -0.0594 0.4362 0.0535 0.4834 -0.0277 0.7167

Reciprocal - x -0.1257 0.0984 -0.1861 0.0139 0.0502 0.5110 -0.1211 0.1113

Double Reciprocal 0.1231 0.1055 0.1711 0.0240 -0.0030 0.9691 0.1333 0.0795

Logarithmic - x 0.0889 0.2432 0.1391 0.0672 -0.0761 0.3186 0.0713 0.3497

Multiplicative 0.0902 0.2363 0.1368 0.0719 -0.0492 0.5193 0.0817 0.2848

Square Root - x 0.0544 0.4756 0.0931 0.2219 -0.0923 0.2256 0.0360 0.6371

Square Root - y 0.0143 0.8519 0.0586 0.4427 -0.0960 0.2078 0.0062 0.9348

S-Curve -0.1251 0.1001 -0.1817 0.0164 0.0267 0.7261 -0.1276 0.0934

Polynomial - order 2 0.2407 0.0061 0.1314 0.2254 0.1399 0.1843 0.3359 0.0118


376

additionally confi rms the conclusions drawn by Kobe et al. (1995), Parent and Messier (1996), and Kobe and Coates (1997) that silver fi r falls in the category of an extremely shade tolerant tree species. Th is characteristic makes silver fi r an exceptionally favorable species for single-tree or group selection (small group) systems, i.e. the protagonist of a specifi c structure of selection forests.

Site conditions have almost no eff ect on the length of stagnation stage, or on the sizes attained by trees in that period. Th e size of tree growth space and, in this sense, the light regime in the stand as the consequence of the applied systems of selection management (single-tree or group selection) are the most eff ective factors infl uencing the duration of the stagnation period and the tree sizes attained in that period. Th e selection system, among other things, also aff ects the size of the tree growth space, more precisely, the light regime in selection forests. For this reason, selection cutting is an instrument by which foresters can infl uence the dynamics of diff erent processes in selection forests (length of stagnation stage, recruitment, transition time, etc.). By increasing the tree growth space, the length of stagnation stage can be shortened, but this simultaneously also increases and accelerates the recruitment and shortens the transition time between diameter classes, which can fi nally lead to the disturbance of the typical selection structure. Consequently, the conservation of the selection structure should be the limiting factor in the process of speeding up the dynamics of selection forest development, and therefore also in the procedure of shortening the period of stagnation stage.

It was also found that the duration of stagnation stage and the tree sizes attained over that period (except for height, and that to a lesser extent) did not have a statistically signifi cant eff ect on the silver fi r

development in the post-stagnation period, which agrees with Magin (1959), and is in contrast to the conclusions drawn by Banković (1981). Th e absence of correlation between these two stages in silver fi r development is a logical consequence of the fact that the fi rst stage (stagnation stage) depends exclusively on the light regime in the forest, while the second stage (post-stagnation period) depends on a series of ecological factors contained in the site class.

Based on the study results and their in-depth analysis, it can be concluded that the initial hypotheses of this research are confi rmed. Th ey are as follows: • Taking into account the time which silver fi r in

selection forests can survive in the latent stage (in the concrete conditions as much as 330 years), this species falls in the category of an extremely shade tolerant tree species;

• Th e analyzed elements of stagnation stage (its length and tree sizes attained over that period) do not depend on site conditions, but primarily on stand conditions, i.e. light regime, as the consequence of the applied selection management system;

• Th ere is no statistically signifi cant correlation between silver fi r development in post-stagnation period and that in stagnation period.

AcknowledgementsWe would like to express our gratitude to the

forestry engineers of the Tara National Park and the Goč Teaching Base for their assistance in the collection of fi eld data. We would also like to thank the Ministry of Science and Environmental Protection of the Republic of Serbia for their fi nancial support during this research as a part of Project 7AG. Th anks are also due to the anonymous reviewers whose suggestions have contributed to the quality of this paper.

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